Lukaku has asked Inter Milan supporters for forgiveness, describing the chance to return to Chelsea as the “chance of a lifetime”.
Lukaku completed a £98 million return to Stamford Bridge on Friday.
Last season, the 28-year-old led Inter to their first Serie A title in a decade.
His departure from the club has left a sour taste with the fans, who defaced his mural outside the San Siro stadium.
However, in an open letter on Sunday, Lukaku said: “I hope you guys understand my decision to move on to Chelsea.
“It’s a chance of a lifetime for me and I think at this time of my career it is a chance that I always dreamed of.”
The Belgian will make his second debut for the Blues this weekend against Arsenal.